Investigation on supersymmetric Pauli-Villars regularization for supersymmetric standard models

Frolov和Slavnov提出的广义Pauli-Villars方法表明了手征规范理论及其超对称扩展的手征对称和规范对称正则化的可能性。通过分析他们的方法，从一般的非特殊化的角度出发，构造了一种广义的Pauli-Villlars正则化方法，阐明了该方法的有效性。我们进一步尝试把它推广到超对称手征规范理论。我们的研究结果可以概括如下：1.推广的Pauli-Villars方法可以应用于一般规范群的理论。当费米子属于无反常表象时，理论可以被正则化而不影响手征对称性和规范对称性。这个结果是非常重要的，因为一般认为手征费米子正则化时，手征对称性与规范对称性是不一致的。对于具有反常费米子含量的理论，这一点是不正确的。 ...更多信息 2.正则化自动产生了横向真空极化张量。此外，费米子数和共形流中出现的反常具有规范不变形式。3.广义Pauli-Villars方法与Fujikawa的协变正则化方法密切相关，因为它明显地保持了规范不变。它再现了协变规范异常。结果表明，我们的方法对各种异常提供了一个更简单的计算格式，但我们还没有成功地将广义Pauli-Villars方法超对称化，这一点还有待进一步研究。目前还不完全清楚这种普遍化是否可能。通过分析协变正则化规范电流的结构，我们得到的结果强烈地表明，将广义Pauli-Villars正则化推广到超对称手征规范理论的可能性。少

The generalized Pauli-Villars method proposed by Frolov and Slavnov suggests the possibility of chiral symmetric as well as gauge symmetric reguralization for chiral gauge theories and their supersymmetric extensions. By analyzing their method from general setting which is not specialized to a particular model, we reconstructed a generalized Pauli-Villlars regularization method, clarifying the validity of this method. We further tried to extend it to supersymmetric chiral gauge theories. The outcome of our investigation can be summarized as follows :1.The generalized Pauli-Villars method can be applied to theories with general gauge group. When fermions belong to an anomaly free representation, the theory can be reguralized without affecting both chiral and gauge symmetries. This result is highly nontrivial because it is generally believed that chiral symmetry can not be consistent with gauge symmetry in regularizing chiral fermions. For theories with anomalous fermion contents, this m … More ethod does not work completely and there arise singular terms in the gauge currents.2.The regularization yields automatically the transverse vacuum polarization tensor. Furthermore, the anomalies appearing in fermion numbers and conformal currents possess gauge invarinat forms.3.The generalized Pauli-Villars method turns out to be intimately related to Fujikawa's covariant regularization method since it preserves manifestly the gauge symmetry.4.A regularization which is manifestly gauge-covariant and supersymmetric can also be formulated for super-symmetric chiral gauge theories. It reproduces covariant gauge anomalies. It turned out that our method provids a simpler computational scheme for various anomalies.We have not succeeded in supersymmetrizing the generalized Pauli-Villars method, which should be investigated further. At present, it is not completely clear whether such generalization is possible or not. Our consequences obtained so far by analyzing the structure of covariantly regularized gauge currents strongly suggest the possibility of extending the generalized Pauli-Villars regularization to supersymmetric chiral gauge theories. Less